Combining Texts

All the ideas for 'The Poverty of Philosophy', 'On Providence' and 'works'

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6 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
For intuitionists excluded middle is an outdated historical convention [Brouwer]
     Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth.
     From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2
     A reaction: [Brouwer 1952:510-11]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]
     Full Idea: In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities.
     From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6
     A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer.
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
To be always happy is to lack knowledge of one half of nature [Seneca]
     Full Idea: To be always happy and to pass through life without any mental distress is to lack knowledge of one half of nature.
     From: Seneca the Younger (On Providence [c.60], §4)
     A reaction: These kind of paradoxes plague virtue theory, and any theory which aims at an ideal. Heaven, for example, seems to have no problems to solve, which spells boredom. The fascination of corrupt people is their superior knowledge of the world.
23. Ethics / C. Virtue Theory / 4. External Goods / a. External goods
Nothing bad can happen to a good man [Seneca]
     Full Idea: Nothing bad can happen to a good man.
     From: Seneca the Younger (On Providence [c.60], §2)
     A reaction: This is a pithy summary of a well know ancient attitude - one that is rejected by Aristotle, but defended by Socrates. It depends what you mean by 'bad' - but that is a rather modern response.
24. Political Theory / D. Ideologies / 11. Capitalism
The handmill gives feudalism, the steam mill capitalism [Marx]
     Full Idea: The handmill gives you society with the feudal lord; the steam mill society with the industrial capitalist.
     From: Karl Marx (The Poverty of Philosophy [1847], p.202), quoted by Peter Singer - Marx 7
     A reaction: If technology dictates social structure, then feudalism is still with us, in low-tech industries. What if the steam mill had been invented in 1300?
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
The ocean changes in volume in proportion to the attraction of the moon [Seneca]
     Full Idea: The waves increase by degrees, approaching to the hour and day proportionately larger or smaller in volume as they are attracted by the star we call the moon, whose power controls the ocean's surge.
     From: Seneca the Younger (On Providence [c.60], §1)
     A reaction: ....just in case anyone thought that Isaac Newton had invented gravity.